Sentence examples for concept of length from inspiring English sources
This generalized concept of length is known as the Lebesgue measure.
Hence, to accept the parallel postulate is to deny the possibility of an absolute concept of length.
So the central problem faced by Lebesgue was not integration as such at all; it was to generalize the concept of length to sufficiently complicated sets.
Poncelet's followers realized that they were hampering themselves, and disguising the true fundamentality of projective geometry, by retaining the concept of length and congruence in their formulations, since projections do not usually preserve them.
Although the cross ratio was used extensively by early 19th-century projective geometers in formulating theorems, it was felt to be a somewhat unsatisfactory concept because its definition depended upon the Euclidean concept of length, a concept from which projective geometers wanted to free the subject altogether.
In the language of the limited question considered, a listing of all sample values (random numbers) of an infinite sequence of statistically independent random variables can be printed out by a Turing machine, at least in the simple case, with strict adherence to the definition of all probabilistic terms as based on measure theory, the theory that generalizes the concept of length.
It would result in "a proliferation of concepts of length, of temperature, and of all other scientific concepts that would not only be practically unmanageable, but theoretically endless".
As a part of this, we attempt to answer the critical questions: are vague shape descriptors representing the concepts of length, width, and height good discriminators of molecular shape?
This is not modesty so much as caution, certainly a function of being 57 and not 39, the age I was when I embarked the last time, with no concept of the length and arduousness of what lay in front of me.
The Euler critical load and the concept of buckling length are extensively used in this context.
